def inv(a, overwrite_a=0):
""" inv(a, overwrite_a=0) -> a_inv
Return inverse of square matrix a.
"""
a1 = asarray_chkfinite(a)
if len(a1.shape) != 2 or a1.shape[0] != a1.shape[1]:
raise ValueError, 'expected square matrix'
overwrite_a = overwrite_a or (a1 is not a and not hasattr(a,'__array__'))
#XXX: I found no advantage or disadvantage of using finv.
## finv, = get_flinalg_funcs(('inv',),(a1,))
## if finv is not None:
## a_inv,info = finv(a1,overwrite_a=overwrite_a)
## if info==0:
## return a_inv
## if info>0: raise LinAlgError, "singular matrix"
## if info<0: raise ValueError,\
## 'illegal value in %-th argument of internal inv.getrf|getri'%(-info)
getrf,getri = get_lapack_funcs(('getrf','getri'),(a1,))
#XXX: C ATLAS versions of getrf/i have rowmajor=1, this could be
# exploited for further optimization. But it will be probably
# a mess. So, a good testing site is required before trying
# to do that.
if getrf.module_name[:7]=='clapack'!=getri.module_name[:7]:
# ATLAS 3.2.1 has getrf but not getri.
lu,piv,info = getrf(transpose(a1),
rowmajor=0,overwrite_a=overwrite_a)
lu = transpose(lu)
else:
lu,piv,info = getrf(a1,overwrite_a=overwrite_a)
if info==0:
if getri.module_name[:7] == 'flapack':
lwork = calc_lwork.getri(getri.prefix,a1.shape[0])
lwork = lwork[1]
# XXX: the following line fixes curious SEGFAULT when
# benchmarking 500x500 matrix inverse. This seems to
# be a bug in LAPACK ?getri routine because if lwork is
# minimal (when using lwork[0] instead of lwork[1]) then
# all tests pass. Further investigation is required if
# more such SEGFAULTs occur.
lwork = int(1.01*lwork)
inv_a,info = getri(lu,piv,
lwork=lwork,overwrite_lu=1)
else: # clapack
inv_a,info = getri(lu,piv,overwrite_lu=1)
if info>0: raise LinAlgError, "singular matrix"
if info<0: raise ValueError,\
'illegal value in %-th argument of internal getrf|getri'%(-info)
return inv_a
def pinv2(a, cond=None):
""" pinv2(a, cond=None) -> a_pinv
Compute the generalized inverse of A using svd.
"""
a = asarray_chkfinite(a)
u, s, vh = decomp.svd(a)
t = u.typecode()
if cond in [None,-1]:
cond = {0: feps*1e3, 1: eps*1e6}[_array_precision[t]]
m,n = a.shape
cutoff = cond*scipy_base.maximum.reduce(s)
psigma = zeros((m,n),t)
for i in range(len(s)):
if s[i] > cutoff:
psigma[i,i] = 1.0/conjugate(s[i])
#XXX: use lapack/blas routines for dot
return transpose(conjugate(dot(dot(u,psigma),vh)))
def toimage(arr,high=255,low=0,cmin=None,cmax=None,pal=None,
mode=None,channel_axis=None):
"""Takes a Numeric array and returns a PIL image. The mode of the
PIL image depends on the array shape, the pal keyword, and the mode
keyword.
For 2-D arrays, if pal is a valid (N,3) byte-array giving the RGB values
(from 0 to 255) then mode='P', otherwise mode='L', unless mode is given
as 'F' or 'I' in which case a float and/or integer array is made
For 3-D arrays, the channel_axis argument tells which dimension of the
array holds the channel data.
For 3-D arrays if one of the dimensions is 3, the mode is 'RGB'
by default or 'YCbCr' if selected.
if the
The Numeric array must be either 2 dimensional or 3 dimensional.
"""
data = asarray(arr)
if iscomplexobj(data):
raise ValueError, "Cannot convert a complex-valued array."
shape = list(data.shape)
valid = len(shape)==2 or ((len(shape)==3) and \
((3 in shape) or (4 in shape)))
assert valid, "Not a suitable array shape for any mode."
if len(shape) == 2:
shape = (shape[1],shape[0]) # columns show up first
if mode == 'F':
image = Image.fromstring(mode,shape,data.astype('f').tostring())
return image
if mode in [None, 'L', 'P']:
bytedata = bytescale(data,high=high,low=low,cmin=cmin,cmax=cmax)
image = Image.fromstring('L',shape,bytedata.tostring())
if pal is not None:
image.putpalette(asarray(pal,typecode=_UInt8).tostring())
# Becomes a mode='P' automagically.
elif mode == 'P': # default gray-scale
pal = arange(0,256,1,typecode='b')[:,NewAxis] * \
ones((3,),typecode='b')[NewAxis,:]
image.putpalette(asarray(pal,typecode=_UInt8).tostring())
return image
if mode == '1': # high input gives threshold for 1
bytedata = ((data > high)*255).astype('b')
image = Image.fromstring('L',shape,bytedata.tostring())
image = image.convert(mode='1')
return image
if cmin is None:
cmin = amin(ravel(data))
if cmax is None:
cmax = amax(ravel(data))
data = (data*1.0 - cmin)*(high-low)/(cmax-cmin) + low
if mode == 'I':
image = Image.fromstring(mode,shape,data.astype('i').tostring())
else:
raise ValueError, _errstr
return image
# if here then 3-d array with a 3 or a 4 in the shape length.
# Check for 3 in datacube shape --- 'RGB' or 'YCbCr'
if channel_axis is None:
if (3 in shape):
ca = Numeric.nonzero(asarray(shape) == 3)[0]
else:
ca = Numeric.nonzero(asarray(shape) == 4)
if len(ca):
ca = ca[0]
else:
raise ValueError, "Could not find channel dimension."
else:
ca = channel_axis
numch = shape[ca]
if numch not in [3,4]:
raise ValueError, "Channel axis dimension is not valid."
bytedata = bytescale(data,high=high,low=low,cmin=cmin,cmax=cmax)
if ca == 2:
strdata = bytedata.tostring()
shape = (shape[1],shape[0])
elif ca == 1:
strdata = transpose(bytedata,(0,2,1)).tostring()
shape = (shape[2],shape[0])
elif ca == 0:
strdata = transpose(bytedata,(1,2,0)).tostring()
shape = (shape[2],shape[1])
if mode is None:
if numch == 3: mode = 'RGB'
else: mode = 'RGBA'
if mode not in ['RGB','RGBA','YCbCr','CMYK']:
raise ValueError, _errstr
if mode in ['RGB', 'YCbCr']:
assert numch == 3, "Invalid array shape for mode."
if mode in ['RGBA', 'CMYK']:
assert numch == 4, "Invalid array shape for mode."
# Here we know data and mode is coorect
image = Image.fromstring(mode, shape, strdata)
return image
